An accurate numerical algorithm for solving compressible three-phase flows in porous media

Abstract

In this paper a numerical method is described for solving the nonlinears system of three-phase compressible flows in orous media in two space dimensions. In order to deal separately with the different physical pricesses,a Spliting metods isused which leads to solve an ahyperbolic and parabolic system .the antidiffusive Harten's scheme enablexs an accurate treatment of the hyperbolic part. whereas finte volumes are used to solve the parabolic system Some numerical results are presents for a two-dimensional problem, where nonlinear interactions between different fluid fronts occur.

Keywords:

• Compressible flows
• porous media,Roe' matrix Riemann problem